Related papers: On a Hyperbolic-Parabolic Parasitoid-Parasite Syst…
We investigate the Lotka-Volterra model for predator-prey competition with a finite carrying capacity that varies periodically in time, modeling seasonal variations in nutrients or food resources. In the absence of time variability, the…
The paper is concerned with a system consisting of two coupled nonlinear parabolic equations with a cross-diffusion term, where the solutions at positive times define the initial states. The equations arise as steady state equations of an…
In this paper, we study the dynamics of the ratio-dependent type prey-predator model with different free boundaries. The two free boundaries, determined by prey and predator respectively, implying that they may intersect each other as time…
This paper addresses a nonlinear partial differential control system arising in population dynamics. The system consist of three diffusion equations describing the evolutions of three biological species: prey, predator, and food for the…
In this paper we investigate some free boundary problems for the Lotka-Volterra type prey-predator model in one space dimension. The main objective is to understand the asymptotic behavior of the two species (prey and predator) spreading…
Consider a species whose population density solves the steady diffusive logistic equation in a heterogeneous environment modeled with the help of a spatially non constant coefficient standing for a resources distribution in a given box. We…
In this study, we investigate a prey-predator model exhibiting Holling type-III functional response among mutually interfering predators to assess the effects of provision of additional food to natural enemies in altering pest dynamics. We…
We consider a predator-prey population model with prey gathering together for defense purposes. A transmissible unrecoverable disease affects the prey. We characterize the system behavior, establishing that ultimately either only the…
An impulsive model of augmentative biological control consisting of a general continuous predator-prey model in ordinary differential equations augmented by a discrete part describing periodic introductions of predators is considered. It is…
The dynamics of predator-prey systems influenced by intra-specific competition and additional food resources have increasingly become a subject of rigorous study in the realm of mathematical biology. In this study, we consider an additional…
We propose and investigate a discrete-time predator-prey system with cooperative hunting in the predator population. The model is constructed from the classical Nicholson-Bailey host-parasitoid system with density dependent growth rate. A…
In this paper, we proposed a population model depicting the dynamics of a prey species showing group defence against a generalist predator. The group defence characteristic is represented by a non-monotonic functional response. We have…
A non-Markovian stochastic predator-prey model is introduced in which the prey are immobile plants and predators are diffusing herbivors. The model is studied by both mean-field approximation (MFA)and computer simulations. The MFA results a…
We prove the well posedness of a class of non linear and non local mixed hyperbolic-parabolic systems in bounded domains, with Dirichlet boundary conditions. In view of control problems, stability estimates on the dependence of solutions on…
This paper considers systems of balance law with a dissipative non local source. A global in time well posedness result is obtained. Estimates on the dependence of solutions from the flow and from the source term are also provided. The…
Predator prey interactions are one of ecology's central research themes, but with many interdisciplinary implications across the social and natural sciences. Here we consider an often-overlooked species in these interactions, namely…
To understand the spreading and interaction of prey and predator, in this paper we study the dynamics of the diffusive Lotka-Volterra type prey-predator model with different free boundaries. These two free boundaries, which may intersect…
In this work we develop a discrete model of competing species affected by a common parasite. We analyze the influence of the fast development of the shared disease on the community dynamics. The model is presented under the form of a two…
This paper is dedicated to the local existence theory of the Cauchy problem for a general class of symmetrizable hyperbolic partially diffusive systems (also called hyperbolic-parabolic systems) in the whole space $\mathbb{R}^d$ with $d\ge…
This paper presents a study of the two-predators-two-preys discrete-time Lotka-Volterra model with self- inhibition terms for preys with direct applications to ecological problems. Parameters in the model are modified so that each of them…